Consider a perfectly competitive market with market supply $Q ^ { 5 } = - 2 + P$ and market demand $Q ^ { d } = 30 - P$ . What is total surplus in this market?

Question

Quizplus · Accepted Answer

To find the total surplus, we need to find the area between the demand and supply curves up to the equilibrium point, which is where demand equals supply. Setting the two equations equal to each other, we get:
30 - P = -2 + P
Solving for P, we get P = 16. Therefore, the equilibrium quantity is:
Q = 30 - 16 = 14
Total surplus can be calculated as the area between the demand and supply curves up to Q = 14. This is equal to:
(1/2)*(16)*(14-4) = 96
We need to add to this the area between the supply curve and the horizontal axis up to Q = 14, which is:
(1/2)*(14)*(16-2) = 84
Therefore, total surplus is 96 + 84 = 180, which is closest to option C (196).

Consider a Perfectly Competitive Market with Market Supply Q5=−2+PQ ^ { 5 } = - 2 + PQ5=−2+P

Consider a Perfectly Competitive Market with Market Supply $Q ^ { 5 } = - 2 + P$